North Carolina has a 3% Sales tax on autos, then you have to pay pseudo "property tax" on the vehicle each year to renew the registration. That would be the standard if you titled the vehicle in NC. I am not sure if you can avoid that 3% sales tax though.
However, Yes you are responsible for paying tax to the state at your county tax rate in order to title/register your vehicle. I don't think Ohio will forgive that 3% you already paid to NC.
Side story...Friend bought a car in Ohio. They paid full county tax on the vehicle (7.75% at the time), Moved to NC a year later. Had to start paying "property tax" on that vehicle (% of the value of the car each year). That is criminal since she already paid full sales tax.
Please keep us posted
miiipilot '16 MG M2, DCT, Exec. Took Delivery 4/30/16